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Question
The number of ordered pairs (α,β), where α,β ∈ (−π,π) satisfying cos(α−β)=1 and cos(α+β)=1e is
The number of ordered pairs (α,β), where α,β ∈ (−π,π) satisfying cos(α−β)=1 and cos(α+β)=1e is
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Solution
The correct option is D 4
Given, (α,β)ϵ(−π,π), and cos(α−β)=1
−2π<α−β<2π,α−β=2nπ
So α−β=0,α=β
Now, cos(α+β)=1e⇒cos2α=1e
So, there are four sets - two in [0.2π) & two is (−2π,0]
So option D is the correct answer
Given, (α,β)ϵ(−π,π), and cos(α−β)=1
−2π<α−β<2π,α−β=2nπ
So α−β=0,α=β
Now, cos(α+β)=1e⇒cos2α=1e
So, there are four sets - two in [0.2π) & two is (−2π,0]
So option D is the correct answer
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